Positivity and negativity of solutions to nxn weighted systems involving the Laplace operator defined on Rn, n>=3

Bénédicte Alziary, Jacqueline Fleckinger, Marie-Hélène Lécureux and Na Wei
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Bénédicte Alziary: TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - Comue de Toulouse - Communauté d'universités et établissements de Toulouse - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement
Jacqueline Fleckinger: TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - Comue de Toulouse - Communauté d'universités et établissements de Toulouse - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement
Marie-Hélène Lécureux: UT2J - Université Toulouse - Jean Jaurès - Comue de Toulouse - Communauté d'universités et établissements de Toulouse
Na Wei: Unknown

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Abstract: We consider the sign of the solutions of a n × n system defined on the whole space ℝ N, N ≥ 3 and a weight function ρ with a positive part decreasing fast enough, where F is a vector of functions, M is a n×n matrix with constant coefficients, not necessarily cooperative, and the weight function ρ is allowed to change sign. We prove that the solutions of the n × n system exist and then we prove the local fundamental positivity and local fundamental negativity of the solutions when {pipe}λ σ1 - λ ρ{pipe} is small enough, where σ 1 is the largest eigenvalue of the constant matrix M and λσ is the "principal" eigenvalue of.

Date: 2012-06-15
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Published in Electronic Journal of Differential Equations, 2012, 101, pp.1-14

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-05472963

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